At least 170 people, most of them fighters based in the Gaza Strip, have been killed since Israel and the Palestinians relaunched formal peace talks in the US city of Annapolis in November.
For its part, Hamas says it has told Egyptian officials it will consider a ceasefire with Israel if it lifts its blockade of the Gaza Strip and ceases military operations in all Palestinian territories.
Mahmoud al-Zahar, a senior Hamas member, travelled to Egypt on Thursday to resume talks with the Egyptian government about the border between the Gaza Strip and Egypt.
Sami Abu Zuhri, a Hamas official, said the group discussed with Egyptian officials this week the possibility of a prisoner swap.
Such a deal could lead to the release of Gilad Shalit, an Israeli soldier seized by Hamas in a 2006 raid, in exchange for the release of hundreds of Palestinians held in Israeli jails.
Last month, Hamas fighters breached Gaza's border with Egypt, temporarily enabling hundreds of thousands of Palestinians to flood parts of Egypt's Sinai border region for 12 days.
On Friday, John Holmes, the UN senior most humanitarian affairs official, said the closure of Gaza has created "grim and miserable" conditions that deprive inhabitants of their basic dignity.
After a tour of Gaza, he urged a reopening of the borders.
Bernard Kouchner, the visiting French foreign minister, has also called for the opening of the Palestinian enclave's borders.
"We are calling to remove the blockade on Gaza because there must be movement for goods and people," he told the Palestinian daily Al Quds in an interview published on Saturday.
"The economic and humanitarian situation in Gaza is bad, and the blockade is affecting the economy in general, and also the living conditions."
The creation of a viable Palestinian state is in Israel's interest, Kouchner said during a tour of Bethlehem in the West Bank on Saturday.
He urged tourists from around the world to visit Jesus' traditional birthplace, as part of efforts to revive the battered Palestinian economy.
Kouchner met the city's mayor, visited a peace centre and toured a French hospital.
He was due to meet Mahmoud Abbas, the Palestinian president, and Salam Fayyad, the prime minister, on Saturday and Israeli officials the following day.